Record Nr.

UNISA996466544803316

Autore

Bernardi Enrico <1838-1900, >

Titolo

Counting statistics for dependent random events : with a focus on finance / / Enrico Bernardi and Silvia Romagnoli

Pubbl/distr/stampa


Cham, Switzerland : , : Springer, , [2021]
©2021

ISBN

3-030-64250-X

Descrizione fisica

1 online resource (213 pages) : illustrations

Disciplina

519.535

Soggetti

Dependence (Statistics)

Copulas (Mathematical statistics)

Finance - Mathematical models

Dependència (Estadística)

Finances

Models matemàtics

Llibres electrònics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

Intro -- Preface -- List of Common Symbols, Notations, and Acronyms -- Contents -- Part I The Main Ingredients -- 1 Clustering -- 1.1 Preliminary on Clustering -- 1.2 The Similarity Measure for Static Data -- 1.3 The Similarity Measure for Time Series -- 1.3.1 Model-Free Approaches -- 1.3.2 Model-Based Approaches -- 1.4 Hierarchical Algorithm -- 1.5 Partitioning Algorithm -- 1.5.1 k-Means Clustering -- 1.6 Neural Network Models -- 1.6.1 Clustering Algorithms -- 1.6.2 Kohonen Self-Organizing Maps -- 1.7 Search-Based Approaches -- 1.7.1 Evolutionary Approaches for Clustering -- 1.7.2 Simulated Annealing Approach -- 1.8 A Clustering Exercise on the European Banking System -- References -- 2 Copula Function and C-Volume -- 2.1 Copula Functions -- 2.1.1 Fréchet-Hoeffding Bounds of a n-Dimensional Copula and Association Measures -- 2.2 Families of Copulas -- 2.2.1 Elliptical Copulas -- Gaussian Copulas -- Student's t Copula -- 2.2.2 Archimedean Copulas -- 2.2.3 Extreme-Value Copulas -- 2.3 Pure Hierarchical Copulas -- 2.4 Hierarchical Grouping Copulas

-- 2.4.1 Clusterized Homogeneous and Clusterized Hierarchical Copulas -- 2.4.2 Hierarchical Kendall Copulas -- 2.5 Volume of an n-Dimensional Copula -- 2.5.1 Clusterized Hierarchical Copulas: CHY-Volume -- 2.6 Example: Homogeneous CHY-Volume Versus CR Algorithm -- 2.6.1 Scalability of the Homogeneous CHY-Based Algorithm -- References -- 3 Combinatorics and Random Matrices: A Brief Review -- 3.1 Combinatoric Distribution of a Random Event -- 3.1.1 Permutations: Ordered Selection -- 3.1.2 Combinations: Unordered Selection -- 3.1.3 The Hardy-Ramanujan Asymptotic Partition Formula -- 3.1.4 The Combinatorial Problem in CHY-Volume Computation -- 3.1.5 Testing Compatibility with the Groups -- 3.2 Random Matrices -- 3.2.1 Gaussian Ensembles -- 3.2.2 An Illustrative Example of a Two-by-Two Random Matrix.

3.2.3 Singular Values of Rectangular Matrices -- 3.2.4 Marchenko-Pastur Distribution -- 3.2.5 The Distorted Combinatoric Distributions -- References -- Part II Mixing the Ingredients: A Recipe for a New Aggregation Algorithm -- 4 Counting a Random Event: Traditional Approach and New Perspectives -- 4.1 Counting Variables: Fundamentals in Literature -- 4.1.1 Generalized Poisson Distribution -- 4.1.2 Compound Poisson Distribution -- 4.2 Counting Process: Fundamentals in Literature -- 4.2.1 Counting Processes in Credit Risk Models: The Intensity-Based Approach -- 4.3 A New Combinatoric Approach for Counting -- 4.3.1 A Counting Variable Linked to a Clusterized Homogeneous Dependence Structure -- 4.3.2 Clusterized Homogeneous Copulas: CHC-Volume -- 4.3.3 Preparing the CHC-Computation -- 4.3.4 CHC and CHY Computation -- 4.3.5 The Volume of a Clusterized Copula: CHC and CHY -- 4.3.6 Pdf of a Counting Variable Linked to a CHC: A Formal Approach -- 4.3.7 The Boxes' Definition for the CHC-Volume Computation -- 4.3.8 The Dynamic Version of the Combinatoric-Approach -- References -- 5 A New Copula-Based Approach for Counting: The Distorted and the Limiting Case -- 5.1 The Distorted Copula-Based Approach: Fatal Event -- 5.1.1 From a Not Distorted to a Distorted Structure: A Probabilistic Discussion -- 5.1.2 Distorted Copula-Based Distribution of a Fatal Counting Variable -- 5.2 The Distorted Copula-Based Approach: Not Fatal Event -- 5.2.1 The Distorted Copula-Based Distribution of a Not Fatal Counting Variable -- 5.2.2 A Pseudo-Spectral Analysis of the Arrival Matrices -- 5.3 High-Dimensional Problems: The Pure Limiting Models -- 5.4 High-Dimensional Problems: The Limiting Clusterized Copulas -- 5.4.1 Hierarchical Limiting Model: A Credit Risk Application -- The Within Classes Computing Step -- The Between Classes Aggregation Step -- Case 1 -- Case 2 -- Case 3.

5.4.2 Hierarchical Hybrid Copulas: A Credit Risk Application -- 5.4.3 Check for the Groups' Cardinality: The HYC Model -- References -- 6 Real Data Empirical Applications -- 6.1 HYC-Based Model for a Worldwide Sovereign Debt Large Portfolio -- 6.2 Risk Evaluation Based on HYC Model: A Credit-Exposed European Investment Portfolio Analysis -- 6.2.1 Copula-Based Loss Distribution -- 6.2.2 Calibration of the Dependencies -- 6.2.3 HYC Model: Portfolio Application -- 6.2.4 HYC-VaR versus CM-VaR: an Empirical In-Sample Experiment -- Hypothesis -- CM Model -- HYC Model -- 6.3 Structural and Marginal Distortion in a Credit-Exposed Portfolio: a DHC Application -- 6.4 A Bayesian Analysis of the DHC Model -- 6.4.1 Multivariate Dependence Calibration -- 6.4.2 The Loss Function: Index Versus Replicating Portfolio -- 6.4.3 A Bayesian Analysis on the Residuals -- References -- References.

Record Nr.

UNINA9910694039203321

Titolo

Roundtable discussion : Hurricane Katrina : hearing of the Committee on Health, Education, Labor, and Pensions, United States Senate, One Hundred Ninth Congress, first session, on examining rebuilding lives and communities after Hurricane Katrina, September 8, 2005

Descrizione fisica

1 online resource (iii, 47 p.)